Longest Increasing Arithmetic Subsequence

You are given an array of integers. Your task is to determine the length of the longest subsequence that forms a strictly increasing arithmetic progression.

An arithmetic progression is a sequence of numbers of the form \(a, a+d, a+2d, \ldots\), where \(d\) (the common difference) is a non-zero constant. The subsequence you choose must have at least two elements to form an arithmetic progression. If the array has fewer than 2 elements, output 0.

Note: The subsequence does not need to be contiguous.

inputFormat

The input is read from stdin as follows:

• The first line contains a single integer \(T\), the number of test cases.
• For each test case, the first line contains an integer \(n\), the number of elements in the array.
• The second line contains \(n\) space-separated integers representing the array.

outputFormat

For each test case, output a single integer on a separate line to stdout representing the length of the longest subsequence that forms a strictly increasing arithmetic progression. If no valid subsequence exists, output 0.

## sample

3
5
1 2 3 4 5
6
1 7 10 13 14 19
4
5 10 15 20

5
4
4

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